| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 15.3.164...536.2 |
$x^{15} - 3 x^{14} - 5 x^{13} + 29 x^{12} - 11 x^{11} + 49 x^{10} - 225 x^{9} + 553 x^{8} - 741 x^{7} + 623 x^{6} - 295 x^{5} + 15 x^{4} + 95 x^{3} - 77 x^{2} + 29 x - 5$ |
$15$ |
[3,6] |
$2^{18}\cdot 11^{10}\cdot 17^{6}$ |
$3$ |
$35.2920879995$ |
$62.75412841824106$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$8$ |
$2231844.9898$ |
| 15.3.164...536.3 |
$x^{15} - 3 x^{14} + 5 x^{13} - 27 x^{12} + 91 x^{11} - 173 x^{10} + 479 x^{9} - 1589 x^{8} + 2907 x^{7} - 4065 x^{6} + 5371 x^{5} - 4533 x^{4} + 1069 x^{3} + 797 x^{2} - 563 x + 73$ |
$15$ |
[3,6] |
$2^{18}\cdot 11^{10}\cdot 17^{6}$ |
$3$ |
$35.2920879995$ |
$62.75412841824106$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$8$ |
$2231844.9898$ |
| 15.15.157...496.2 |
$x^{15} - 3 x^{14} - 43 x^{13} + 153 x^{12} + 581 x^{11} - 2639 x^{10} - 2341 x^{9} + 19385 x^{8} - 6025 x^{7} - 61505 x^{6} + 59207 x^{5} + 64819 x^{4} - 102309 x^{3} + 8607 x^{2} + 29313 x - 8357$ |
$15$ |
[15,0] |
$2^{14}\cdot 67^{6}\cdot 101^{6}$ |
$3$ |
$65.0309052977$ |
$157.09393470243788$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$14$ |
$1351880002.32$ |
| 15.15.157...496.3 |
$x^{15} - x^{14} - 47 x^{13} + 5 x^{12} + 691 x^{11} + 125 x^{10} - 4109 x^{9} - 1347 x^{8} + 9621 x^{7} + 6549 x^{6} - 7671 x^{5} - 9401 x^{4} - 1483 x^{3} + 1945 x^{2} + 985 x + 139$ |
$15$ |
[15,0] |
$2^{14}\cdot 67^{6}\cdot 101^{6}$ |
$3$ |
$65.0309052977$ |
$157.09393470243788$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$14$ |
$1351880002.32$ |
| 15.3.605...241.1 |
$x^{15} - 18 x^{13} - 477 x^{11} - 4551 x^{10} - 5103 x^{9} + 107811 x^{8} + 675537 x^{7} + 1019238 x^{6} - 6688395 x^{5} - 45591102 x^{4} - 144815383 x^{3} - 281605005 x^{2} - 315011013 x - 152252029$ |
$15$ |
[3,6] |
$3^{20}\cdot 1609^{6}$ |
$2$ |
$82.9438309933$ |
$173.55602508012973$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
$[3]$ |
$2$ |
$8$ |
$84559284.0776$ |
| 15.3.605...241.2 |
$x^{15} - 96 x^{13} - 13 x^{12} + 4203 x^{11} + 417 x^{10} - 99113 x^{9} + 16263 x^{8} + 1286655 x^{7} - 972656 x^{6} - 8508177 x^{5} + 9764478 x^{4} + 23747884 x^{3} - 26735256 x^{2} - 22983852 x - 26273539$ |
$15$ |
[3,6] |
$3^{20}\cdot 1609^{6}$ |
$2$ |
$82.9438309933$ |
$173.55602508012973$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
$[3]$ |
$2$ |
$8$ |
$84559284.0776$ |
| 15.15.211...736.1 |
$x^{15} - 114 x^{13} - 100 x^{12} + 4482 x^{11} + 3708 x^{10} - 88484 x^{9} - 40062 x^{8} + 968490 x^{7} - 43996 x^{6} - 5713620 x^{5} + 3124686 x^{4} + 15082908 x^{3} - 14728854 x^{2} - 7371504 x + 8794506$ |
$15$ |
[15,0] |
$2^{14}\cdot 3^{16}\cdot 7^{10}\cdot 101^{6}$ |
$4$ |
$142.89528879891552$ |
$253.0242658113988$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
$[3]$ |
$2$ |
$14$ |
$388996704805.6018$ |
| 15.15.211...736.2 |
$x^{15} - 114 x^{13} - 100 x^{12} + 4482 x^{11} + 3708 x^{10} - 88484 x^{9} - 40062 x^{8} + 968490 x^{7} - 43996 x^{6} - 5713620 x^{5} + 3124686 x^{4} + 15082908 x^{3} - 14728854 x^{2} - 7371504 x + 8794506$ |
$15$ |
[15,0] |
$2^{14}\cdot 3^{16}\cdot 7^{10}\cdot 101^{6}$ |
$4$ |
$142.89528879891552$ |
$253.0242658113988$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
$[3]$ |
$2$ |
$14$ |
$388996704805.6018$ |
| 15.15.211...736.3 |
$x^{15} - 126 x^{13} - 260 x^{12} + 5094 x^{11} + 18504 x^{10} - 63044 x^{9} - 359514 x^{8} - 53280 x^{7} + 1842012 x^{6} + 2118888 x^{5} - 1967676 x^{4} - 3976168 x^{3} - 1327692 x^{2} + 347604 x + 162996$ |
$15$ |
[15,0] |
$2^{14}\cdot 3^{16}\cdot 7^{10}\cdot 101^{6}$ |
$4$ |
$142.89528879891552$ |
$253.0242658113988$ |
|
|
? |
$\GL(2,4):C_2$ (as 15T21) |
$[3]$ |
$2$ |
$14$ |
$388996704805.6018$ |
| 15.3.445...096.1 |
$x^{15} - 111 x^{13} - 386 x^{12} + 4374 x^{11} + 32124 x^{10} + 8031 x^{9} - 758232 x^{8} - 4623792 x^{7} - 11819488 x^{6} + 19768680 x^{5} + 172734582 x^{4} + 106696493 x^{3} - 692358768 x^{2} - 545123220 x + 1098864488$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{20}\cdot 89^{10}$ |
$3$ |
$150.1685568934579$ |
$172.49837427579374$ |
|
|
|
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$8$ |
$27429793198.236717$ |
| 15.3.445...096.2 |
$x^{15} - 111 x^{13} - 386 x^{12} + 4374 x^{11} + 32124 x^{10} + 8031 x^{9} - 758232 x^{8} - 4623792 x^{7} - 11819488 x^{6} + 19768680 x^{5} + 172734582 x^{4} + 106696493 x^{3} - 692358768 x^{2} - 545123220 x + 1098864488$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{20}\cdot 89^{10}$ |
$3$ |
$150.1685568934579$ |
$172.49837427579374$ |
|
|
|
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$8$ |
$27429793198.236717$ |
| 15.3.445...096.3 |
$x^{15} + 39 x^{13} - 126 x^{12} - 828 x^{11} - 2742 x^{10} + 17813 x^{9} + 337554 x^{8} - 1656558 x^{7} + 5545194 x^{6} - 13770792 x^{5} + 171154476 x^{4} - 122660067 x^{3} + 390948876 x^{2} - 2630278944 x + 197201216$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{20}\cdot 89^{10}$ |
$3$ |
$150.1685568934579$ |
$172.49837427579374$ |
|
|
|
$\GL(2,4):C_2$ (as 15T21) |
trivial |
$2$ |
$8$ |
$27429793198.236717$ |
| 15.3.109...000.1 |
$x^{15} - 6 x^{14} + 134 x^{13} - 1932 x^{12} + 39232 x^{11} + 1914040 x^{10} + 24548432 x^{9} + 188094312 x^{8} - 2085029776 x^{7} - 22326553544 x^{6} + 110819295040 x^{5} + 2950874619616 x^{4} + 18735138209396 x^{3} - 192452928680008 x^{2} - 1165670534162352 x + 6404254997206928$ |
$15$ |
[3,6] |
$2^{24}\cdot 5^{10}\cdot 7^{10}\cdot 109^{10}$ |
$4$ |
$740.1351352348216$ |
$870.0643085922301$ |
|
|
|
$\GL(2,4):C_2$ (as 15T21) |
$[3, 3, 6]$ |
$2$ |
$8$ |
$980069639469857.5$ |
| 15.3.109...000.2 |
$x^{15} - 6 x^{14} + 134 x^{13} - 1932 x^{12} + 39232 x^{11} + 1914040 x^{10} + 24548432 x^{9} + 188094312 x^{8} - 2085029776 x^{7} - 22326553544 x^{6} + 110819295040 x^{5} + 2950874619616 x^{4} + 18735138209396 x^{3} - 192452928680008 x^{2} - 1165670534162352 x + 6404254997206928$ |
$15$ |
[3,6] |
$2^{24}\cdot 5^{10}\cdot 7^{10}\cdot 109^{10}$ |
$4$ |
$740.1351352348216$ |
$870.0643085922301$ |
|
|
|
$\GL(2,4):C_2$ (as 15T21) |
$[3, 3, 6]$ |
$2$ |
$8$ |
$980069639469857.5$ |
| 15.3.109...000.3 |
$x^{15} - 6 x^{14} + 134 x^{13} - 1932 x^{12} + 39232 x^{11} - 1687320 x^{10} + 14110592 x^{9} + 116006072 x^{8} - 1661717376 x^{7} + 51011785656 x^{6} + 225636633760 x^{5} - 2958541580064 x^{4} - 3695478657164 x^{3} - 153026634530248 x^{2} - 2269510517234192 x - 5107245000273072$ |
$15$ |
[3,6] |
$2^{24}\cdot 5^{10}\cdot 7^{10}\cdot 109^{10}$ |
$4$ |
$740.1351352348216$ |
$870.0643085922301$ |
|
|
|
$\GL(2,4):C_2$ (as 15T21) |
$[3, 3, 3]$ |
$2$ |
$8$ |
$1960139278939715.0$ |
